Magnetization reversal phenomenon of higher-order lump and mixed interaction structures on periodic background in the (2+1)-dimensional Heisenberg ferromagnet spin equation

Abstract

This paper mainly researches a useful model that can describe the rapid magnetization reversal process, namely the (2+1)-dimensional Heisenberg ferromagnet spin equation. Based on its Lax pair, we construct the iterative generalized (r,N−r)-fold Darboux transformation (DT), and obtain new position-controllable higher-order lump, periodic wave and rich mixed lump–breather interaction structures on periodic background. In particular, with the increase of N in the iterative generalized (r,N−r)-fold DT, we find that the structure of the lump and periodic wave can flip over with respect to the background. Moreover, we also find a bright lump structure with two peaks and two valleys, which does not flip with the increase of N. We study the magnetization trajectory and magnetization on the Bloch sphere, from which we discover that the magnetization is distributed in an incomplete unit sphere for the flipped case, while the magnetization is distributed in a complete unit sphere for the non-flipped case. These magnetization reversal phenomena are expected to have potential applications in understanding the rapid magnetization reversal process.